Piecewise Smooth $N$-Dimensional Nonlinear Singular Singularly Perturbed Boundary Value Problems

Abstract

Internal layer phenomena are often appear in various piecewise smooth nonlinear singular singularly perturbed problems of natural sciences. To characterize these special structures, we study piecewise smooth $n$-dimensional nonlinear singular singularly perturbed boundary value problems. In particular, we show the existence of solutions with an internal layer and construct their asymptotic expansions. The remainder estimations of the approximate solutions are also given. Finally, an example aimed to verify the correctness of the developed theory is presented.